MATRICES AND t pOER OF 66UARE reix:
DETeRmiNANTSs
A-2, A' =A3.A. -
Highut rey
Ls A Qys try fo <reate
patter in m a r k .
SiNGULAR MATRX
HRANS POse OF MArRIX
JAL=o) 2-|
A=
3 2J
RACE OF MATRX 31
32
+
CA) =TrCA')
) (A +B+ C) = A+ eT r
*2) frcKA) KTY.(A) (AB)= B. AT
3) Tr. A B) = .(A)+ Tr. cB)
(AB=CT, B. AT
) Y. (A8) = Ty. (BA)
(ABcO)T =p.CT, gT.AT
MOLÍpiCArÍON OF MATRIK (A= (A),
MATeix*
SKer - Sy mneTRiC
AB =-BA ABanti-commute
|A =A ’ Symmetric
=-AT
A)B=A(<8) =K(AB)
z
’A(Bt) = Aß AC
(A+ (Ae
’ (A+B)==A2AB+BA Sro
+B2
Symm y 2
=A2 AB+BA-e
’(At e (A -9)
Nol
DETeRmiNANTSs
A-2, A' =A3.A. -
Highut rey
Ls A Qys try fo <reate
patter in m a r k .
SiNGULAR MATRX
HRANS POse OF MArRIX
JAL=o) 2-|
A=
3 2J
RACE OF MATRX 31
32
+
CA) =TrCA')
) (A +B+ C) = A+ eT r
*2) frcKA) KTY.(A) (AB)= B. AT
3) Tr. A B) = .(A)+ Tr. cB)
(AB=CT, B. AT
) Y. (A8) = Ty. (BA)
(ABcO)T =p.CT, gT.AT
MOLÍpiCArÍON OF MATRIK (A= (A),
MATeix*
SKer - Sy mneTRiC
AB =-BA ABanti-commute
|A =A ’ Symmetric
=-AT
A)B=A(<8) =K(AB)
z
’A(Bt) = Aß AC
(A+ (Ae
’ (A+B)==A2AB+BA Sro
+B2
Symm y 2
=A2 AB+BA-e
’(At e (A -9)
Nol
